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Properties

Label 3800.2.di
Level $3800$
Weight $2$
Character orbit 3800.di
Rep. character $\chi_{3800}(37,\cdot)$
Character field $\Q(\zeta_{20})$
Dimension $4768$
Sturm bound $1200$

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Defining parameters

Level: \( N \) \(=\) \( 3800 = 2^{3} \cdot 5^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3800.di (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 3800 \)
Character field: \(\Q(\zeta_{20})\)
Sturm bound: \(1200\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(3800, [\chi])\).

Total New Old
Modular forms 4832 4832 0
Cusp forms 4768 4768 0
Eisenstein series 64 64 0

Trace form

\( 4768 q - 20 q^{4} - 12 q^{6} - 32 q^{7} - 40 q^{9} + O(q^{10}) \) \( 4768 q - 20 q^{4} - 12 q^{6} - 32 q^{7} - 40 q^{9} - 12 q^{16} - 32 q^{17} + 20 q^{20} - 32 q^{23} - 32 q^{25} - 32 q^{26} - 20 q^{28} - 36 q^{30} - 44 q^{36} - 36 q^{38} - 40 q^{39} + 4 q^{42} - 160 q^{44} + 16 q^{47} - 20 q^{54} - 72 q^{55} - 28 q^{57} + 40 q^{58} - 104 q^{62} - 64 q^{63} + 40 q^{64} - 60 q^{66} - 60 q^{68} - 32 q^{73} + 4 q^{80} + 1104 q^{81} - 4 q^{82} - 168 q^{87} + 148 q^{92} + 28 q^{95} + 28 q^{96} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{2}^{\mathrm{new}}(3800, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.